{"id":"91f67b99-5c4d-4164-be2f-b0ad9963cea5","arxiv_id":"1908.07596","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"Using partial-wave unitarity to bound the valid energy range of SMEFT and HEFT operators, the thesis finds non-empty discovery regions for beyond-Standard-Model effects in same-sign WW scattering at HL-LHC and HE-LHC.","lead":"This thesis computes how far effective field theory can be trusted in same-sign W boson scattering at the LHC, and finds that new physics could still be discovered within that range at both the planned high-luminosity and high-energy phases. It offers a method to define discovery regions that respect the theory's validity, which could shape how future collider data are interpreted.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The non-emptiness claim rests on using the on-shell unitarity scale as a cutoff for the full off-shell process; the Sec. 7.1.3 polarization-completeness argument is only asymptotic and is never tested quantitatively.","rationale":"The central claim is that non-empty discovery regions exist for every EFT basis when the EFT is used only up to its unitarity bound. The weakest part of that argument is the identification of the unitarity bound from on-shell WW scattering with the validity boundary of the full off-shell process. The reader's weakest assumption identifies exactly this on-shell-to-off-shell mapping and the tree-level unitarity cutoff. I agree with that assessment. The polarization completeness identity in Eq. (7.7) is a true decomposition, but the subsequent step that keeps only the on-shell physical polarizations is an approximation whose accuracy is not quantified in the paper. The numerical cross-checks with VBFNLO, FeynRules, and FeynCalc are genuine supporting evidence for the on-shell amplitude computations, but they do not validate the off-shell-to-on-shell mapping in the phase-space region that drives the discovery significance. The concern is not an internal inconsistency; it is a load-bearing, untested approximation. If the proposed reweighting test shows the significance is robust to removing auxiliary polarizations or cutting on virtualities, the central claim stands. Absent that test, CONDITIONAL is the appropriate verdict, matching the reader's recommendation, so no verdict change is needed.","tokens_in":64056,"tokens_out":8406,"duration_ms":119660,"concrete_test":"Recompute the expected significance for one representative SMEFT model (e.g. OS0 at f = 1 TeV^-4, HL-LHC) with two modifications: (i) add a cut on reconstructed W off-shellness, e.g. |k_i^2 - m_W^2|/m_W^2 < 4, and (ii) repeat the calculation retaining only the physical polarizations (lambda = -, +, 0) in the numerator decomposition of Eq. (7.10), dropping the auxiliary-polarization contributions. If either modification removes or substantially shrinks the 5-sigma region, the non-emptiness claim is an artifact of the on-shell proxy. As a complementary check, compare the m_WW distribution of the full 2->4 amplitude to the on-shell-approximated distribution in the region m_WW < sqrt(sU) and verify agreement at the few-percent level.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Sec. 7.1.3 argues that qualitative features of the full pp -> 2j + l nu l' nu' process can be inferred from on-shell W+W+ scattering by using the polarization completeness identity (Eq. 7.7). The argument is asymptotic: for fast Ws the auxiliary polarization epsilon_A becomes proportional to the longitudinal polarization, and the propagators suppress large off-shellness. But the central discovery-region analysis then applies the on-shell tree-level unitarity bound sqrt(sU) as a hard cutoff on the WW invariant mass in the full 2->4 process. This is not justified by the identity alone. In qq -> qq W* W* events, the individual W virtualities k_i^2 are not bounded by m_WW^2; they can be much larger than m_W^2 even when m_WW < sqrt(sU). For those events the decomposition (7.10) contains non-negligible auxiliary-polarization contributions that have no on-shell counterpart, so the amplitude is not the on-shell amplitude whose partial waves were bounded by (4.34)/(4.36). If the EFT expansion parameter is set by the largest off-shell momentum rather than by m_WW, the true breakdown scale can be lower than sqrt(sU). The non-emptiness of the discovery regions is therefore conditional on an untested quantitative assumption: that off-shell effects do not change the unitarity cutoff enough to remove the 5-sigma regions. The paper itself only gives the asymptotic argument and no numerical validation of the equivalence in the phase-space region used for the significance calculation.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This doctoral thesis develops an EFT analysis of same-sign W pair production in pp→2j+W*W*→2j+lνl'ν' at HL-LHC and HE-LHC, using both SMEFT and HEFT bases. It defines EFT 'models' as the SM plus one dimension-8 (SMEFT) or dp=8 (HEFT) genuine quartic gauge coupling operator. In Ch. 4 it derives perturbative partial-wave unitarity bounds, and in Ch. 7.1 it computes on-shell W+W+→W+W+ and W+W−→W+W− amplitudes to define for each model a validity scale √sU(f_i) from the diagonalized |Re T|≤1/2 bound. The discovery-region analysis of Sec. 7.2 then restricts the full off-shell process to m_WW<√sU and finds, for every operator studied, values of the Wilson coefficient for which the expected significance exceeds 5σ. The thesis also compares SMEFT versus HEFT polarization signatures, identifying e.g. the T42/T44 enhancement of −−00 and −+00 fractions as a distinct non-linear feature, and studies the gain from HE-LHC.","tokens_in":64351,"tokens_out":11812,"duration_ms":317492,"significance":"The paper has real strengths: the helicity-amplitude calculations are detailed and cross-checked against VBFNLO, FeynRules, and FeynCalc; the unitarity analysis includes both same- and opposite-sign WW scattering and uses helicity-space diagonalization; and the main output is a set of falsifiable predictions (non-empty discovery regions) rather than only exclusion limits. If the validity-cutoff prescription survives scrutiny, the non-emptiness result is an important, non-obvious statement: it indicates that EFT searches in VBS can be sensitive to BSM physics even when the EFT is used only up to its unitarity bound, and the SMEFT/HEFT signature comparison provides a useful discriminator between linear and non-linear electroweak symmetry breaking. The thesis is largely a compilation of published papers [a-d], but the self-contained derivation of the unitarity framework gives it added value as a reference.","major_comments":[{"comment":"The central non-emptiness claim depends on using the on-shell unitarity scale √sU as a hard upper cutoff on the WW invariant mass in the off-shell process. The argument in Sec. 7.1.3 is asymptotic and does not quantitatively control the decomposition in Eq. (7.10): the propagator suppression of large k_i^2 is not the same as a bound on the individual virtualities, and the auxiliary-polarization amplitudes in Eq. (7.10) have no on-shell counterpart whose partial waves were constrained by Eqs. (4.34)/(4.36). Events with one W far off shell can therefore contribute to the selected sample even when m_WW<√sU, and if the EFT expansion parameter is controlled by the largest k_i^2 rather than by m_WW, the true breakdown scale can lie below √sU, changing or emptying the 5σ regions. The manuscript provides no numerical validation of the equivalence, such as distributions of k_i^2 in the signal region or a comparison of the full off-shell amplitudes with their on-shell approximation as a function of m_WW. Please add such a check, or restrict the significance calculation to a phase-space region where the on-shell mapping is demonstrated.","section":"Sec. 7.1.3, Eq. (7.7)-(7.10); Sec. 7.2"},{"comment":"The paper identifies the EFT validity limit with the scale at which the tree-level partial waves violate |Re T|≤1/2. This is a standard and useful criterion, but it is a necessary rather than a sufficient condition: loop corrections in a non-renormalizable EFT can become large before the tree-level bound is saturated, particularly for dimension-8 operators whose amplitudes grow as s^2/Λ^4 and for which the loop expansion parameter near √sU can be O(1); the √sU values in Tables 7.1-7.2 are a few TeV, so s/(16π^2v^2) is not parametrically small. Since the discovery regions are defined by integrating up to √sU, an earlier actual breakdown would shrink them. Please state explicitly that √sU is an upper bound on the validity region and provide an estimate of the size of one-loop corrections, or an NDA-based argument, showing that the bound is not over-optimistic.","section":"Sec. 4, Eqs. (4.34)/(4.36); Sec. 7.2"}],"minor_comments":[{"comment":"The printed formula for the auxiliary polarization is malformed: the denominator as typeset, k^2−m_W^2 k^2 m_W^2, is not a well-formed expression and should be replaced by a single square-root formula, presumably √(k^2(k^2−m_W^2)) or the intended equivalent.","section":"Eq. (7.8)"},{"comment":"The cross-references to 'Sec. 1', 'Sec. 2', ..., 'Sec. 7' do not match the actual chapter numbering (the Standard Model is Ch. 2, the conclusions are Ch. 8, etc.). Please correct the section cross-references.","section":"Chapter 1 (Introduction)"},{"comment":"The units quoted for the Wilson coefficients are inconsistent: the captions write 'TeV4' where TeV^{-4} is meant for the dimension-8 SMEFT coefficients, while the HEFT operators have TeV^{-2} or dimensionless coefficients. Please standardize the notation for f_i and c_i throughout.","section":"Tables 7.1-7.2 and appendix tables"},{"comment":"A short summary table in the main text listing the final discovery regions (operator, sign of f_i, f_i range, √sU range, and maximum significance) would greatly improve readability, since the numerical results are otherwise distributed over long appendices.","section":"Sec. 7.2 and figures"}],"recommendation":"major_revision","confidential_remarks":"The main request, a quantitative validation of the off-shell to on-shell mapping, goes to the heart of the thesis's novel method and is appropriate for a major revision. The thesis is based on already published papers [a-d]; the referee report treats the thesis as the primary document. No additional concerns about scope or attribution."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Punchline: this is a doctoral thesis, not a new research paper. It is built directly on the author's published work [a-d], and the introduction says so. What it adds is a unified write-up, full appendices, and a more explicit statement of the logic connecting on-shell WW partial-wave unitarity to the discovery regions in pp -> 2j + l nu l' nu'. If you need the details behind [a-d], this is a convenient single document; if you are looking for a new result, you won't find one.\n\nThe strengths are real. The amplitude computations are carefully cross-checked with VBFNLO, FeynRules, and FeynCalc. The unitarity analysis goes beyond the usual j=0 projection by diagonalizing in helicity space, and it combines same-sign with opposite-sign WW scattering, which matters because the same operators affect both. The SMEFT vs HEFT comparison of polarised cross sections is well explained, and the T42/T44 distinction is a nice phenomenological handle on the linear/non-linear Higgs question. The appendices contain enough analytic material that a competent reader can reproduce the main numbers. The citation pattern is honest: the thesis explicitly credits [a-d] and does not dress them up as new.\n\nThe main soft spot is exactly the one the stress-test note identifies. The discovery regions are defined with the on-shell tree-level unitarity scale sqrt(sU) as a cutoff on the WW invariant mass. The justification in Sec. 7.1.3 is an asymptotic polarization-completeness argument: in the fast-W limit the auxiliary polarization approaches the longitudinal one, and propagators suppress large off-shellness. That is plausible, but it is not a quantitative proof for the 2->4 phase space. Individual W virtualities can be large even when m_WW < sqrt(sU), and the EFT expansion parameter in the full amplitude is not obviously m_WW. The thesis never shows that the 5-sigma regions survive a more conservative cutoff on individual virtualities. I do not think this kills the paper; it is a curable gap. But the non-emptiness claim is conditional on it, and a serious referee should ask for that test.\n\nMinor caveat: the discovery-region plots are not visible in the text I read, which limits independent verification of the numerical results.\n\nWho is this for? EFT phenomenologists working on VBS, LHC analysts planning HL/HE-LHC searches, and PhD students wanting a thorough walk-through. It deserves a serious referee, not a desk reject, but the referee should treat it as a thesis document and request the off-shell robustness check rather than expecting a new research claim.","headline":"A careful, self-contained doctoral thesis built from the author's own prior papers, whose central non-empty discovery-region claim rests on an on-shell unitarity cutoff that is plausible but never quantitatively validated for off-shell W's.","tokens_in":64894,"tokens_out":3637,"would_cite":true,"duration_ms":556512,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This thesis claims that same-sign WW scattering at the HL-LHC and HE-LHC can discover new physics described by single dimension-8 EFT operators, provided the EFT is used only up to the energy scale where perturbative unitarity breaks down.","keywords":["vector boson scattering","same-sign WW scattering","effective field theory","SMEFT","HEFT","dimension-8 operators","partial wave unitarity","HL-LHC discovery potential"],"falsifier":"Compute the full off-shell matrix elements for pp -> 2j + l nu_l l' nu'_l keeping the auxiliary polarization state in Eq. (7.7) and check whether the on-shell approximation reproduces the high-MWW region; if off-shell contributions are not suppressed by the propagators, the sqrt(sU) cutoff is wrong. Alternatively, measure the WW invariant mass distribution at the HL-LHC: if a 5-sigma excess attributed to a single dimension-8 operator appears only for MWW above the sqrt(sU) of the best-fit Wilson coefficient, the EFT is being used beyond its claimed validity and the non-empty discovery-region conclusion fails.","tokens_in":63799,"feed_emoji":"⚛️","tokens_out":6421,"duration_ms":62683,"temperature":0.7,"pith_summary":"This dissertation asks whether the effective-field-theory program can discover new physics in vector-boson scattering before the EFT itself loses predictive power. The author studies the process pp -> 2 jets + W* W* -> 2 jets + l nu_l l' nu'_l at the HL-LHC and HE-LHC, taking each EFT 'model' to be the Standard Model plus a single dimension-8 operator (SMEFT) or single dp=8 operator (HEFT) that modifies quartic gauge couplings only. The central claim is that when the EFT is used only up to the energy scale sqrt(sU) at which tree-level partial-wave unitarity is violated, every one of the studied models still has a non-empty discovery region: there are Wilson-coefficient values for which the expected significance exceeds 5 sigma. This matters because it shows the EFT approach to WW scattering is not self-defeating: the new-physics signal appears at energies where the EFT is still a valid description, and the method gives a procedure for defining search regions consistently. The thesis also provides a comparison of SMEFT and HEFT experimental signatures and shows how discovery regions change when the pp collision energy is increased.","feed_headline":"WW scattering finds new physics before EFT breaks down","feed_subtitle":"Using dimension-8 operators only up to their unitarity bound, 5-sigma discovery regions exist at HL-LHC and HE-LHC.","key_machinery":"The central object is the EFT 'model': the Standard Model Lagrangian plus one genuine quartic-gauge-coupling operator (dimension-8 in SMEFT, primary dimension dp=8 in HEFT), with a Wilson coefficient f_i. The argument runs through the on-shell elastic W+W+ -> W+W+ helicity amplitudes and their partial-wave projections: tree-level amplitudes that grow with energy violate perturbative unitarity at a scale $\\sqrt$(sU), and this scale sets the upper end of the EFT's validity, $Lambda^{2}$ <= sU. The polarization completeness identity (Eq. 7.7) connects these on-shell amplitudes to the off-shell process pp -> 2j + l nu_l l' nu'_l, justifying the transfer of qualitative and quantitative conclusions. For each operator, the paper derives analytic leading-energy forms of helicity amplitudes and partial waves, identifies which helicity configuration violates unitarity first, and uses that to define $\\sqrt$(sU), then computes expected significances at HL-LHC and HE-LHC with the EFT truncated at that scale.","core_discovery":"Using the EFT only in its region of validity, the expected significance of the dimension-8 (or dp=8) genuine quartic-gauge-coupling effects in same-sign WW scattering can exceed 5 sigma at the HL-LHC or HE-LHC for every single-operator EFT model considered, regardless of whether the SMEFT or HEFT basis is chosen. The region of validity is defined by the perturbative partial-wave unitarity bound sqrt(sU), computed from on-shell W+W+ and W+W- scattering amplitudes, including the stronger of the same- and opposite-sign limits and, in most cases, a helicity-space diagonalization of partial waves. The off-shell LHC process is related to the on-shell amplitudes through the polarization completeness identity, so that far off-shell contributions are suppressed and the qualitative behavior is governed by on-shell helicity amplitudes. The thesis presents the resulting discovery regions in the Wilson-coefficient space, compares SMEFT and HEFT signatures, and shows that raising the pp collision energy from 14 TeV (HL-LHC) to 27 TeV (HE-LHC) enlarges the discovery regions.","pith_inferences":["If the off-shell-to-on-shell mapping holds, the same discovery-region method transfers to other VBS channels such as WZ and ZZ scattering, and to future lepton colliders, because the polarization completeness identity is process-independent, though the amplitude set must be re-derived.","A measurement of final-state W polarizations in same-sign WW events could discriminate not only SMEFT from HEFT but also the S, M, and T operator classes within each basis, since the thesis shows distinct saturating helicity configurations for each class.","The single-operator truncation becomes more defensible if positivity bounds hold, because they imply dimension-8 gQGC coefficients can dominate dimension-6 ones; the thesis cites these bounds as motivation but does not rely on them for the main claim.","A null result at the HL-LHC at 5 sigma would exclude the studied single-operator models only within their unitarity-limited parameter space, leaving open the possibility of effects at larger Wilson coefficients where the EFT description is no longer valid."],"forward_implications":["For each of the single-operator SMEFT and HEFT models studied, there is at least one Wilson-coefficient value for which the expected significance at the HL-LHC is above 5 sigma even though the EFT is used only up to its unitarity bound.","The correct validity scale for WW-scattering EFT analyses is the stronger unitarity limit from both same-sign and opposite-sign WW scattering, not the same-sign process alone; for M-type operators the opposite-sign channel provides the limiting bound.","Raising the pp collision energy from 14 TeV (HL-LHC) to 27 TeV (HE-LHC) moves and generally enlarges the discovery regions in the Wilson-coefficient space.","SMEFT and HEFT give different experimental signatures in same-sign WW scattering; in particular, the HEFT operators T42 and T44 enhance the --00 and -+00 polarization fractions, which is not seen for the SMEFT dimension-8 operators.","The proposed method for defining discovery regions is in principle not limited to the single-operator truncation and can be applied to models with several operators of arbitrary dimension, although the thesis works out the single-operator case."],"supporting_citations":[{"why":"Establishes the same-sign WW discovery-potential method in SMEFT and the use of the unitarity bound for the HL-LHC.","marker":"[a]"},{"why":"Extends the analysis to the HEFT basis and the dp=8 gQGC operators, including the SMEFT-HEFT comparison.","marker":"[b]"},{"why":"Provides the HL-LHC and HE-LHC Higgs physics context used for the collision-energy comparison.","marker":"[c]"},{"why":"Gives the HE-LHC discovery-region results for the same-sign WW process.","marker":"[d]"},{"why":"Supplies the complete HEFT operator classification used to select the gQGC operators (P6, P11, T42 through T62).","marker":"[25]"},{"why":"Defines the primary dimension counting that justifies choosing dp=8 HEFT operators and links operator structure to cross-section impact.","marker":"[97]"},{"why":"Provides the SMEFT dimension-8 gQGC operator basis (OS0 through OT2) used to define the SMEFT models.","marker":"[120]"},{"why":"VBFNLO is used to cross-check the unitarity-limit computations with a 1-degree angular cut.","marker":"[121]"}],"fun_headline_variants":["WW scattering probes new physics within EFT validity","Dim-8 WW scattering: 5-sigma discovery within EFT bounds","Same-sign WW scattering: EFT-valid dim-8 reach 5-sigma","WW scattering at HL-LHC/HE-LHC: 5-sigma via valid EFT"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole discovery-region calculation assumes that the on-shell W+W+ scattering amplitudes, cut off at the energy where tree-level perturbative unitarity fails, faithfully describe the full off-shell LHC process pp -> 2j + l nu_l l' nu'_l; if far off-shell W's contribute significantly, or if loop effects extend the EFT's range, the discovery regions are miscalibrated.","fun_headline_variants_meta":{"raw":{"variants":["WW scattering probes new physics within EFT validity","Dim-8 WW scattering: 5-sigma discovery within EFT bounds","Same-sign WW scattering: EFT-valid dim-8 reach 5-sigma","WW scattering at HL-LHC/HE-LHC: 5-sigma via valid EFT"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00045,"raw_usage":{"total_tokens":2282,"prompt_tokens":975,"completion_tokens":1307,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":591,"completion_tokens_details":{"reasoning_tokens":1224}},"tokens_in":591,"tokens_out":1307,"duration_ms":11352,"temperature":1.0,"reasoning_tokens":1224,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T12:01:45.942661+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the full off-shell matrix elements for pp -> 2j + l nu_l l' nu'_l keeping the auxiliary polarization state in Eq. (7.7) and check whether the on-shell approximation reproduces the high-MWW region; if off-shell contributions are not suppressed by the propagators, the sqrt(sU) cutoff is wrong. Alternatively, measure the WW invariant mass distribution at the HL-LHC: if a 5-sigma excess attributed to a single dimension-8 operator appears only for MWW above the sqrt(sU) of the best-fit Wilson coefficient, the EFT is being used beyond its claimed validity and the non-empty discovery-region conclusion fails.","supporting_citations":[],"review_version":1}